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13. Latitude at Meridian Passage

13. Latitude at Meridian Passage. Presented By: MATE O. Course Outline. Navigational Astronomy Lecture 1 & 2 Mean Time / Apparent Time Lecture 3 Time Zones, Zone Description, Chronometer Time Lecture 4 The Earth, Celestial, And Horizon Coordinate System Lecture 5 & 6

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13. Latitude at Meridian Passage

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  1. 13. Latitude at Meridian Passage Presented By: MATE O

  2. Course Outline • Navigational Astronomy Lecture 1 & 2 • Mean Time / Apparent Time Lecture 3 • Time Zones, Zone Description, Chronometer Time Lecture 4 • The Earth, Celestial, And Horizon Coordinate System Lecture 5 & 6 • The Spherical Triangle Lecture 7 • Circle of Equal Altitude Intercept Lecture 8 • Time Diagram, Right Ascension Lecture 9 • The Nautical Almanac, Finding GHA, LHA, and Dec. Lecture 10 & 11 • Instruments For Celestial Navigation Lecture 12 • Sight Reduction of the Sun, Stars, Planets, Moon Lecture 13 - 15 • Plotting and Advancing / Retarding the Assumed Position Lecture 16 • Calculating Time of Meridian Passage (LAN) Lecture 17 • Calculating Latitude at Meridian Passage Lecture 18 • Calculating Time of Sunrise/ Sunset/ Twilight Lecture 19 • Star Shooting Schedule / Pub. 249 Lecture 20 • Azimuth and Amplitudes Lecture 21 – 24 • Polaris – Azimuth and Latitude By Lecture 25 • Star – Finder – Stars, Planets, Selecting the 3 best Stars Lecture 26 • The Complete Day’s Work Lecture 27 & 28

  3. VIII: Local Apparent Noon LAN • “LAN” Or Local Apparent Noon (Or “LAM” Midnight) Is Useful To The Navigator. It Is A Time When An Observation Of The Sun Will Obtain A Latitude Line Of Position. • Local Apparent Noon Occurs When The Visible (Apparent) Sun Is Over The Upper Branch Of The Observer’s Meridian. The Local Hour Angle Of The Sun Is 000°. • Local Apparent Midnight Occurs When The Visible (Apparent) Sun Is Over The Lower Branch Of The Observer’s Meridian. The Local Hour Angle Of The Sun Is 180°. • Usually The Sun Is Only Visible During Local Apparent Noon. In High Latitudes And Depending On The Time Of Year , The Sun Can Be Observed At Noon And Midnight.

  4. VIII: Meridian Transit Meridian Transit • The Meridian Transit Of A Celestial Body Is When The Body Is Directly Passing Over The Upper Branch Or The Lower Branch Of The Observer’s Local Meridian • Upper Transit Is When The Body Passes Over The Longitude Of The Observer. • Lower Transit Is When The Body Passes Over The Longitude On The Other Side Of The Earth (180° From His Longitude). The Lower Branch Of His Meridian Is The Other Half Of A Meridian (Great Circle). It Is The Other Half Of The Great Circle That Passes Through His Position On The Other Side Of The Poles.

  5. VIII: Local Apparent Noon Time of LAN • In Order To Accurately Observe The Celestial Body As It Passes At Meridian Transit It Is Important To Calculate The Exact Time Of Passage. • There Are Different Methods Of Determining Time Of Meridian Transit (LAN). The Easiest Method To Use Is The GHA Interpolation Method. • Another Method Often Used Is The DLO Method. • We Will Discuss Both Methods.

  6. VIII: Local Apparent Noon GHA Method of Determining Time of LAN • GHA Method Of Determining LAN • Steps: • First Estimate: • Find DR Longitude For 1200 ZT. • Using This DR Longitude We Can Determine What GHA Is Necessary To Make LHA = 000° For Upper Transit (LAN) • In Order To Determine LHA In West Longitude We Subtract Our Longitude From GHA. In Order To Determine LHA In East Longitude We Add Our Longitude To GHA. • So If We Are In West Longitude, Finding The GHA Of The Body That Is Equal To Our Longitude Will Result In A LHA Of 000° • In East Longitude, Finding The GHA Of The Body That Is Equal To Our Longitude Subtracted From 360° Will Result In A LHA Of 000°. • Second Estimate • For A More Accurate Time You May Repeat Steps 1-5 Using A New DR Position For The Time Of First Estimate

  7. VIII: Local Apparent Noon GHA Method of Determining Time of LAN • GHA Method Of Determining LAN • Example: On 7 February 1981, your 0800 ZT DR Position is Lat. 22° 16.0’N, λ 092° 26.0’W. Your Vessel is on Course 270° T at a speed of 20.0 kts. What is the ZT of Local Apparent Noon. • Steps 1. Find 1200 DR Longitude = 093° 58.0’W 2. In West Longitude find the time where the GHA is equal to your Longitude. 3. We see that it will fall between 1800 and 1900 GMT 1800 086° 26.9’ 18?? 093° 58.0’ Arc diff b/w λ and 1800 GHA = 7° 31.1’ 1900 101° 26.9’ Time diff = 30m 05s So the GMT time of LAN is 1830-05 ZD (+6) -6 (rev.) ZT of LAN 1230-05

  8. VIII: Local Apparent Noon GHA Method of Determining Time of LAN • GHA Method Of Determining LAN • Example: On 14 March 1981, your 0900 ZT DR Position is Lat. 23° 16.0’N, λ 146° 12.0’E. Your Vessel is on Course 286° T at a speed of 14.5 kts. What is the ZT of Local Apparent Noon. • Steps 1. Find 1200 DR Longitude = 145° 36.0’E 2. In East Longitude find the time where the GHA is equal to your Longitude subtracted from 360°. 360° - 145° 36.0’E = 214° 24.0’ 3. We see that it will fall between 0200 and 0300 GMT 0200 207° 39.6’ 02??214° 24.0’ Arc diff b/w λ and 0200 GHA = 6° 44.4’ 0300 222° 39.8’ Time diff = 27 minutes So the GMT time of LAN is 0227 ZD (-10) +10 (rev.) ZT of LAN 1227

  9. VIII: Local Apparent Noon DLO Method of Determining Time of LAN • DLO Method Of Determining LAN • Although not as accurate as the GHA Method Some People Prefer To Use The DLO Method Of Determining LAN Because It Is Easier To Visualize The Passage Of The Body Over Their Meridian In Relation To The Body’s Passage Over The Central Meridian. • To Use The DLO Method Of Determining Time Of LAN – The Time Of Meridian Passage (Mer. Pass) Must Be Determined From The Lower Right Corner Of The Almanac. This Is The Time Of Passage Of The Apparent Sun Over The Central Meridian. • All That Is Required Is Finding Your DLO From The Central Meridian At The Time Of Meridian Passage And Converting This DLO Arc To Time. • Subtract the time from the time of Mer. Pass. If You Are East Of The Central Meridian. • Add the time to the time of Mer. Pass if you are West of the Central Meridian.

  10. VIII: Local Apparent Noon DLO Method of Determining Time of LAN • DLO Method Of Determining LAN Example: On 31 January 1981, your 0920 zone time DR position is LAT 24° 16.0’ S, λ 151° 33.0’ E. Your vessel is on course 258° T at a speed of 18.5 kts. What is the zone time of local apparent noon (LAN)? First find your DR position at the time of Mer. Pass. 1214 L 24° 27.0’S λ 150° 45.0’ E Central Meridian 150° E DR λ 150° 45.0’ E 1214 – 00s - 3 - 00s Ans. 1211-00 ApparentSun 1214 DLO = 0° 45.0’ of Arc to the East or 3 minutes of time The Apparent Sun will be over the Central Meridian at 1214, So It Will Cross our DR λ 3 minutes before 1214

  11. VIII: Latitude Latitude at Meridian Passage Calculating Latitude At Meridian Passage (LAN) • At Meridian Passage It Is Easy To Determine Your Latitude By Knowing The Declination Of The Body And Your Zenith Distance. • Remember That At Meridian Passage The Body Is On Your Meridian, So It Is Located Due North Or Due South Of You. • Observe Meridian Passage And Calculate Apparent Altitude (Ho) Of The Sight. • Calculate Your Zenith Distance By Subtracting Ho From 90°. Your Zenith Distance Is Equal To Your Distance From The Geographic Location Of The Body. • By Knowing The Declination Of The Body At The Time Of The Sight You Know Where The Body Is Located North Or South Of The Equator • So Knowing Where The Body Is Located North Or South Of The Equator And Your Distance From The Body You Can Calculate Your Latitude. • The Formulas Used: Zenith Distance = 90° - Ho Latitude = Declination + Or – Zenith Distance

  12. VIII: Latitude Latitude at Meridian Passage Calculating Latitude At Meridian Passage (LAN) • When Observing The Body Facing South The Zenith Distance Is Labeled North • When Observing The Body Facing North The Zenith Distance Is Labeled South • To Find Latitude: Combine Zenith Distance And Declination According To Their Signs: 1. If The Signs Are The Same Add 2. If The Signs Are Contrary Subtract The Smaller From The Larger And Keep The Sign Of The Larger Example: If The Declination Of The Sun Is 5° North And The Zenith Distance Is 20° South The Latitude Of The Observer Is 15° South. Observer’s Meridian Declination 5° N Equator Zenith Distance 20° S Latitude 15° S

  13. VIII: Latitude Latitude at Meridian Passage Example: On 22 February 1981 LAN occurs at 1147 ZT, Your Zone Description is +3. The Ho of the Sight is 73° 33.3’. You are facing due North at the time of the sight. What is the calculated Latitude at LAN? LAN ZT 1147 ZD +3 GMT 1447 Dec. S 10° 05.4’ 90° 00.0’ d (-.9) -.7 - Ho 73° 33.3’ Dec. S 10° 04.7’ Zenith Dist. 16° 26.7’ S Latitude = Declination S 10° 04.7’ + or - Zenith Dist. S 16° 26.7’ Signs are the Same (ADD) S 26° 31.4’ Observer’s Meridian Equator Declination 10° 04.7’ S Latitude 26° 31.4’ S Zenith Distance 16° 26.7’ S

  14. VIII: Latitude Latitude at Meridian Passage Example: On 15 November 1981 LAN occurs at 1118 ZT, Your Zone Description is +5. The Ho of the Sight is 49° 46.0’. You are facing due South at the time of the sight. What is the calculated Latitude at LAN? LAN ZT 1118 ZD + 5 GMT 1618 Dec. S 18° 34.5’ 90° 00.0’ d (+.6) +.2 - Ho 49° 46.0’ Dec. S 18° 34.7’ Zenith Dist. 40° 14.0’ N Latitude = Declination S 18° 34.7’ + or - Zenith Dist. N 40° 14.0’ Signs are Opposite (Subtract) N 21° 39.3’ Keep the Sign of the Larger Observer’s Meridian Latitude 21° 39.3’ N Zenith Distance 40° 14.0’ N Equator Declination 18° 34.7’ S

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